Programming the Quadratic Formula into the TI-83/84
Name
For those times when a numeric approximation to the solution of a quadratic equation will suffice, using a
programmable calculator to automatically compute and simplify the quadratic formula is rather convenient. Since
we shall expand upon the programmable features of the TI-83/84 throughout the course this is a good starting
point.  = ENTER
COMMAND
COMMENTS
Press PRGM
Brings up the Program Menu: EXEC EDIT NEW
Select NEW 
Use EDIT to edit an existing program
Name = QF 
Names the program QF. Other names will also suffice.
:ClrHome 
PRGM → I/O → 8. Clears the home screen.
:a+bi 
MODE → a+bi. Sets the TI-83+ to Complex mode.
:Disp "SOLVES Ax2 + Bx + C = 0" 
PRGM → I/O → 3. Displays message on the screen.
:Prompt A,B,C 
PRGM → I/O → 2. Will prompt the user for A, B and C
2
:(B −4AC) D 
Calculates the Discriminant
:(-B+√(D))/(2A)P 
Calculates the first root
:(-B−√(D))/(2A)Q 
Calculates the second root.
:Disp "ROOTS",P Frac ,Q Frac 
PRGM → I/O → 3. Displays the two roots.
Now let's run the program. Use PGRM → EXEC → Select Program . Note: For these examples, MODE was
preset to FLOAT accuracy.
Example 1
Solve 2x2 = 9(x + 2)
Rewrite in Standard Form: 2x2 − 9x − 18 = 0
We identify A = 2, B = -9 and C = -18
PGRM → EXEC → QF 
Note: Pressing ENTER at the conclusion of a program will rerun a fresh version of the program.
Example 2
Solve x2 + 2 = 2x
Rewrite in Standard Form: x2 − 2x + 2 = 0
We identify A = 1, B = -2 and C = 2
PGRM → EXEC → QF 
Extra Credit: Use algebra to write the equation in standard quadratic form (ax2 + bx + c = 0). Then use the
Quadratic Formula program to solve the equation.
1.
x2 + x = 42
2.
x2 + 10 = 11x
3.
t2 + 8 = 4t
4.
2x( x – 5 ) = 12
5.
2x2 + 3 = 2(x – x2) + 10
6.
5x
=2
x2 + 1
7.
( x + 3 ) ( 3x + 5 ) = 7
8.
( x + 3 ) ( x – 2 ) = 50
9.
5(x + 1)
9x =
+ 2x
2
10.
x2 = 4x – 53
11.
2
x+4 =x–2
12.
x+7 =x+1
13.
2+
2x – 1 = x
14.
4+
2x2 – 8 = 0
15.
4x(x – 1) + 1 = 0
16.
1+
x2 – 2x + 1 = x